Dynamic positional information: Patterning mechanism versus precision in gradient-driven systems

Optogenetic manipulation of nuclear Dorsal reveals temporal requirements and consequences for transcription

Morphogen gradients convey essential spatial information during tissue patterning. While both concentration and timing of morphogen exposure are crucial, how cells interpret these graded inputs remains challenging to address. We employed an optogenetic system to acutely and reversibly modulate the nuclear concentration of the morphogen Dorsal (DL), homologue of NF-κB, which orchestrates dorso-ventral patterning in the Drosophila embryo. By controlling DL nuclear concentration while simultaneously recording target gene outputs in real time, we identified a critical window for DL action that is required to instruct patterning, and characterized the resulting effect on spatio-temporal transcription of target genes in terms of timing, coordination, and bursting. We found that a transient decrease in nuclear DL levels at nuclear cycle 13 leads to reduced expression of the mesoderm-associated gene snail (sna) and partial derepression of the neurogenic ectoderm-associated target short gastrulation ( sog) in ventral regions. Surprisingly, the mispatterning elicited by this transient change in DL is detectable at the level of single cell transcriptional bursting kinetics, specifically affecting long inter-burst durations. Our approach of using temporally-resolved and reversible modulation of a morphogen in vivo , combined with mathematical modeling, establishes a framework for understanding the stimulus-response relationships that govern embryonic patterning.

Scale invariance in early embryonic development

The expression of a few key genes determines the body plan of the fruit fly. We show that the spatial expression patterns for several of these genes scale precisely with embryo size. Discrete positional markers such as the peaks in striped patterns or the boundaries of expression domains have positions along the embryo's major axis proportional to embryo length, accurate to within 1%. Further, the information (in bits) that graded patterns of expression provide about a cell's position can be decomposed into information about fractional or scaled position and information about absolute position or embryo length; all information available is about scaled position, with [Formula: see text]2% error. These findings imply that the underlying genetic network's behavior exhibits scale invariance in a more precise mathematical sense. We argue that models that can explain this scale invariance also have a "zero mode" in the dynamics of gene expression, and this connects to observations on the spatial correlation of fluctuations in expression levels.

The impact of cell size on morphogen gradient precision

Tissue patterning during embryonic development is remarkably precise. Here, we numerically determine the impact of the cell diameter, gradient length and the morphogen source on the variability of morphogen gradients. We show that the positional error increases with the gradient length relative to the size of the morphogen source, and with the square root of the cell diameter and the readout position. We provide theoretical explanations for these relationships, and show that they enable high patterning precision over developmental time for readouts that scale with expanding tissue domains, as observed in the Drosophila wing disc. Our analysis suggests that epithelial tissues generally achieve higher patterning precision with small cross-sectional cell areas. An extensive survey of measured apical cell areas shows that they are indeed small in developing tissues that are patterned by morphogen gradients. Enhanced precision may thus have led to the emergence of pseudostratification in epithelia, a phenomenon for which the evolutionary benefit had so far remained elusive.

Relationship between epithelial organization and morphogen interpretation

Despite molecular noise and genetic differences between individuals, developmental outcomes are remarkably constant. Decades of research has focused on the underlying mechanisms that ensure this precision and robustness. Recent quantifications of chemical gradients and epithelial cell shapes provide novel insights into the basis of precise development. In this review, we argue that these two aspects may be linked in epithelial morphogenesis.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

Tissue tectonics and the multi-scale regulation of developmental timing

Development encompasses processes that occur at multiple length scales, including gene-regulatory interactions, cell movements and reorganization, cell signalling and growth. It is essential that the timing of events in all of these different processes is coordinated to generate well-patterned tissues and organs. However, how the timing of intrinsic cell state changes is coordinated with events occurring at the multi-tissue and whole-organism level is unknown. Here, we argue that an important mechanism that accounts for the integration of timing across levels of organization is provided by tissue tectonics, i.e. how morphogenetic events driving tissue shape changes result in the relative displacement of signalling and responding tissues and coordinate developmental timing across scales. In doing so, tissue tectonics provides a mechanism by which the cell specification events intrinsic to cells can be modulated by the temporal exposure to extracellular signals. This exposure is in turn regulated by higher-order properties of the embryo, such as their physical properties, rates of growth and the combination of dynamic cell behaviours, impacting tissue morphogenesis. Tissue tectonics creates a downward flow of information from higher to lower levels of biological organization, providing an instance of downward causation in development.

Implications of diffusion and time-varying morphogen gradients for the dynamic positioning and precision of bistable gene expression boundaries

The earliest models for how morphogen gradients guide embryonic patterning failed to account for experimental observations of temporal refinement in gene expression domains. Following theoretical and experimental work in this area, dynamic positional information has emerged as a conceptual framework to discuss how cells process spatiotemporal inputs into downstream patterns. Here, we show that diffusion determines the mathematical means by which bistable gene expression boundaries shift over time, and therefore how cells interpret positional information conferred from morphogen concentration. First, we introduce a metric for assessing reproducibility in boundary placement or precision in systems where gene products do not diffuse, but where morphogen concentrations are permitted to change in time. We show that the dynamics of the gradient affect the sensitivity of the final pattern to variation in initial conditions, with slower gradients reducing the sensitivity. Second, we allow gene products to diffuse and consider gene expression boundaries as propagating wavefronts with velocity modulated by local morphogen concentration. We harness this perspective to approximate a PDE model as an ODE that captures the position of the boundary in time, and demonstrate the approach with a preexisting model for Hunchback patterning in fruit fly embryos. We then propose a design that employs antiparallel morphogen gradients to achieve accurate boundary placement that is robust to scaling. Throughout our work we draw attention to tradeoffs among initial conditions, boundary positioning, and the relative timescales of network and gradient evolution. We conclude by suggesting that mathematical theory should serve to clarify not just our quantitative, but also our intuitive understanding of patterning processes.